So far, so good in the first major offensive of President Barack Obama's war in Afghanistan. For the past four days, 4,000 U.S. Marines and 650 Afghan soldiers have been fighting their way into the southern reaches of Afghanistan's Helmand River valley, hoping to clear out insurgents there. But other than in one limited area of fierce resistance, the fighting has generally been restricted to small-scale skirmishes in which few Taliban have been killed because most of the insurgents appear to have slipped away  as guerrillas tend to do when confronted by overwhelming firepower. More important to U.S. goals, however, is that no civilians have been hurt, since the purpose of the operation is to secure the local population against the Taliban.

Even though he says it's too early to predict success, General Stanley McChrystal, the new commander of U.S. and NATO forces in Afghanistan, is satisfied that the Helmand mission is moving in the right direction. "The operations are not aimed at the enemy force. They are aimed at taking away the population from the enemy," he told TIME. "What we are trying to do is change the dynamics in the area where we are operating." In order to do that, Marines are leaving their armored humvees and sitting down with village elders and tribal leaders to assess their needs, and assuring them that this time the Americans will be sticking around. (See pictures of the new U.S. offensive.)

Operation Khanjar  Pashto for "dagger"  is the first test of the Obama Administration's new strategy for Afghanistan. No longer treated as a concern secondary to Iraq, the Afghanistan theater will see the number of American soldiers serving there increase by 17,000 by this fall. And under McChrystal, they'll be waging a different kind of war. Limited troop availability in the past meant that while NATO forces could clear an area of insurgents, they were unable to hold the terrain. Now the plan is for the Marines to set up combat posts in villages to provide the residents with lasting security. Still, some Afghans are skeptical. "I hope this operation gives a positive result," says Haji Nimatullah, a businessman in Lashkar Gah, the capital of Helmand province, by telephone. "But I am not optimistic. [These] operations are like the cat-and-mouse cartoon where the mouse escapes when the cat attacks, but when the cat is gone, the mouse comes back and starts again." (See pictures of challenges British troops were facing in Helmand in 2008.)

But the U.S. forces are aware of the danger cited by Nimatullah. "What makes Operation Khanjar different from those that have occurred before is the massive size of the force introduced, the speed at which it will insert, and the fact that where we go we will stay and where we stay we will hold, build and work toward transition of all security responsibilities to Afghan forces," said Brigadier General Larry Nicholson, the Marine commander, in a statement.

So far, only one Marine has been killed and several have been wounded. (In eastern Afghanistan, a U.S. soldier appears to have been captured by the Taliban in an event unrelated to the Helmand operation.) Casualty figures will probably rise, however, because the Taliban, having declined to go toe-to-toe with the Marines and instead having melted into the civilian population, will probably resort to asymmetrical warfare tactics like using improvised explosive devices (IEDs). On Saturday, an IED strike killed two U.S. troops in eastern Afghanistan, while another on Thursday killed two British troops elsewhere in Helmand. Stationing Marines among the local population will increase the risk of such attacks, until U.S. forces are able to win over residents through providing development aid and security. To do so, they will have to overcome deeply entrenched suspicions of American aims in the region and resentment of civilian casualties inflicted during previous U.S. operations. "This operation will cause even more insecurity," says Joma Khan, a 32-year-old unemployed man in Lashkar Gah. "Because when people lose their family members or their houses get destroyed, then they join Taliban." (Read "Diplomatic Surge: Can Obama's Team Tame the Taliban?")

Aware of the danger, McChrystal has made the protection of civilians the central tenet of his new approach to fighting the Taliban, even going so far as to limit the use of aerial bombardment to the most extreme circumstances  a turnabout for U.S. ground forces that have grown dependent on air support. McChrystal has also declared  in a soon-to-be-released tactical directive  that soldiers should hold their fire if there is even the slightest risk of a civilian presence in the target zone. "Suppose the insurgent occupies an enemy home or village and engages you from there with the clear idea that when you respond, you are going to create collateral damage," explains McChrystal. "He's going to blame that on you. Even if you kill the insurgents, what happens is you have made the insurgency wider. You are going to run into more IEDs. You are going to run into more insurgents, [and] at the end of the day, you are going to suffer more casualties."

The new directive will certainly make the fight harder in the short term, but it is winning kudos from Afghans. "Already I am hearing a lot of positive feedback [about the Helmand operation]," says Afghanistan's Interior Minister, Hanif Atmar. "What was actually very well received and welcomed by the Afghan people was that [McChrystal] placed a benchmark for his success: he would like to measure his success in terms of how much he has protected the population, how much security he is providing them."

The Marines, however, are a temporary solution. They will remain in Helmand at least through the Afghan presidential elections slated for Aug. 20, when they will assist the Afghan security forces to secure polling places in anticipation of Taliban attacks. What happens beyond that, however, remains a question. "The military can help set the conditions for success, but it is not sufficient for success," U.S. ambassador and former Combined Forces Command Afghanistan (CFC-A) commander Karl Eikenberry told TIME. "The military can help deliver security, but the military in and of itself cannot deliver a lasting peace, cannot deliver an accountable respected government, cannot deliver the necessary set of social services and sustainable economy that only the civilian side can provide for."

The next step in the new Afghan war will be a comprehensive strategy that helps the Afghan government deliver the stability that comes from economic opportunity and a working justice system that will allow Afghans to benefit from those opportunities. That kind of strategy, however, takes far more time than a military operation and requires patience  on the part of both Afghans and the U.S. Administration, which is footing the bill.

The original version of this article mistakenly identified Karl Eikenberry as the former commander of the International Security Assistance Force in Afghanistan. Eikenberry was in fact the commander of the Combined Forces Command Afghanistan (CFC-A).